Problem: Solve for $x$ : $4x^2 - 24x - 64 = 0$
Solution: Dividing both sides by $4$ gives: $ x^2 {-6}x {-16} = 0 $ The coefficient on the $x$ term is $-6$ and the constant term is $-16$ , so we need to find two numbers that add up to $-6$ and multiply to $-16$ The two numbers $-8$ and $2$ satisfy both conditions: $ {-8} + {2} = {-6} $ $ {-8} \times {2} = {-16} $ $(x {-8}) (x + {2}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -8) (x + 2) = 0$ $x - 8 = 0$ or $x + 2 = 0$ Thus, $x = 8$ and $x = -2$ are the solutions.